Alessandro Zocco

We present a more detailed numerical analysis of the global GENE-3D simulations of Bähner et al (the W7-X Team) 2026 Nucl. Fusion 66 016007, focusing on turbulent heat and particle transport and the role of the equilibrium radial electric field across mirror ratio and rotational transform ( ι ) configuration scans in Wendelstein 7-X (W7-X). Ion and electron heat fluxes show only mild sensitivity to both configuration parameters. The particle flux, however, exhibits a pronounced dependence on the mirror ratio, with the low-mirror configuration driving a strong inward particle pinch and the high-mirror configuration producing a net outward flux. Density fluctuation levels at fixed plasma profiles do not reproduce the experimentally observed configuration dependence in the mirror scan, a discrepancy that can be understood in terms of the simulations not satisfying power balance. A synthetic phase contrast imaging (PCI) diagnostic applied to the simulations reproduces the experimental ordering of the wavenumber and frequency spectra in the ι scan but not in the mirror scan, consistent with the same interpretation. The equilibrium radial electric field modifies turbulent transport, with the largest effect on the electron heat flux in regions of strong E × B shear. A controlled parametric study, in which the E r profile is systematically varied in amplitude and radial location, confirms that transport suppression follows the classical shear decorrelation criterion, being strongest where the shear rate exceeds the linear growth rate over the widest radial extent.

12Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here, we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations in an asymptotic expansion in the ratio of transit (bounce) frequency to the mode frequency for ions (electrons), capable of describing two common instabilities: the ion-temperature-gradient (ITG) mode and trapped-electron mode (TEM), in the electrostatic limit. The dispersion relation, which is valid in arbitrary toroidal geometry, takes into account resonances with the magnetic ion and bounce-averaged electron drifts, incorporates non-local effects along the magnetic field line, is valid for arbitrary sign of the growth rate and magnetic curvature, and is shown to satisfy a variational property. Several common approximation models are introduced for both the magnetic drift and finite Larmor radius (FLR) damping, with the Padé approximation for FLR effect in particular resulting in remarkable agreement with the baseline dispersion relation model at significantly reduced costs. The baseline model is verified by comparing solutions of the dispersion relation model to high-fidelity linear gyrokinetic simulations, where the exact eigenfunction of the electrostatic potential from simulations is used as a trial function, showing good quantitative agreement for ITGs and TEMs in shaped tokamaks as well as low-magnetic-shear stellarators.

We investigate the impact of fast ions on turbulent transport in Wendelstein 7-X (W7-X) using the gyrokinetic code GENE, building on earlier findings of fast-ion stabilization of ITG turbulence and focusing on hydrogen minority heating in a Helium-4 plasma, motivated by upcoming ion cyclotron resonance frequency (ICRF) experiments at W7-X. Nonlinear simulations show that moderate fast-ion densities and temperature gradients reduce electron and ion heat fluxes by up to 40%–50%. However, beyond a threshold in fast-ion concentration or gradient strength, the fast-ion heat flux increases sharply and becomes a dominant contribution to the total turbulent transport. Linear simulations reveal that this transition is associated with the emergence of a fast-ion-driven mode, localized in regions of unfavorable magnetic curvature. The mode is driven by fast-ion temperature and density gradients, and arises from a resonance involving both binormal magnetic curvature and parallel advection—the latter being important in W7-X but typically negligible in tokamaks. These results demonstrate that fast-ion effects depend sensitively on their drive: while they can effectively stabilize thermal turbulence, sufficiently strong gradients can trigger fast-ion-dominated transport that limits confinement improvement. The findings provide insight into ICRF heating scenarios in W7-X and fast-ion effects on turbulence in optimized stellarators more generally.

In this work, the interplay between fast ions and safety factor rational surfaces is studied in a turbulent plasma via global nonlinear gyrokinetic simulations. The fast particle-induced enhancement of shearing structures from turbulence self-interaction is analyzed. Our study takes into account the competition between this mechanism and other fast ions effects, i.e. thermal profiles dilution and quasi-resonant interaction. We find the reduction of the zonal modes destabilization threshold caused by fast ions [T. S. Hahm et al, 2023 Phys. Plasmas 30 072501] to be a very effective method to suppress turbulence. Indeed, it leads to the formation of regions where turbulent transport is reduced by 90% of its original value. Furthermore, an n=m=1 fishbone is driven unstable inside the plasma and its interaction with turbulence is studied. We find the beat-driven zonal structure generated by this mode to further reduce turbulence when its presence does not drastically flatten the thermal profiles.

Gyrokinetic simulations of a turbulence-reduced Wendelstein 7-X discharge—characterized by a steep density gradient, moderate temperature gradients, and low plasma beta—show that microtearing mode (MTM) turbulence dominates transport. The simulated heat and particle fluxes agree with experimental measurements, leaving MTMs as the only mode consistent with the data. These conditions, the quasi-isodynamic and nearly max- J magnetic configuration of the Wendelstein 7-X stabilize ion temperature gradient modes and density-gradient-driven trapped-electron modes, while moderate collisionality and low magnetic shear further enable MTM growth. Further nonlinear scans of the density gradient reveal a significant reduction in turbulent transport at the experimentally observed threshold, which we identify as an ion temperature gradient to MTM-dominated turbulence transition. These findings provide a robust explanation for the turbulence suppression and deepen our understanding of low turbulent transport regimes in optimized stellarators.

Transitions to core-electron-root-confinement (CERC) regime are examined in the presence of low-order rational values of the rotational transform (ι) in Wendelstein 7-X. Experiments at densities and heating powers near the bifurcation from pure ion-root to CERC conditions revealed transitions at stationary plasma conditions but evolving plasma currents. Analysis of the effects due to the ramping plasma current indicates a change of the ι profile temporarily crossing low-order rational values. The transition occurs within a narrow range of plasma currents and, supported by simulations of the shielding current evolution, is consistent with the observed rise in central electron temperature. Prior to these transitions, low-frequency fluctuations were detected, ceasing once higher electron temperatures were reached, and the central radial electric field became positive. Experimental and numerical analyses suggest that these fluctuations are not instabilities, but rather sidebands of zonal flow oscillations, Doppler-shifted by the ambient electric field. Although the oscillations are not the trigger, their systematic characterization offers deeper insight into the underlying physics governing the transition and emphasizes the role of the evolving ι.

Line-integrated density fluctuation measurements from the core of the optimised stellarator Wendelstein 7-X (W7-X) are studied in the context of magnetic field geometry changes. The amplitude as well as the spectral distribution of fluctuations is affected by varying the magnetic field configuration. Weaker turbulent fluctuations are observed in configurations with higher rotational transform and lower magnetic mirror depth. Simulations with the gyrokinetic codes stella and GENE-3D are used to investigate the role of magnetic geometry for the experimental observations. The stabilising effect of the high rational transform configuration is reproduced by simulations and can be associated with stronger shaping of the magnetic field. This leads to increased finite Larmor radius and local shear effects, which limit the toroidal extent of ion temperature gradient (ITG) modes. For W7-X configurations with higher magnetic mirror depth, gyrokinetic theory and simulations predict weaker fluctuations, since they are closer to having the maximum- J property, which has a stabilising effect on trapped-electron mode and ITG. The opposite trend is observed experimentally, which can therefore not be explained by geometry effects on turbulence alone.